A brushless motor used in an electric power steering apparatus, etc., is controlled by supplying an electric current to a stator coil in accordance with a rotation angle of a rotor. There is thus known a rotation angle detection device such as that shown in FIG. 13 (see, for example, Patent Document 1). The rotation angle detection device has a rotor 1, which includes a magnet having two magnetic poles, and two magnetic sensors 11 and 12 disposed at an angular interval of 90° centered about a central rotation axis of the rotor 1. The respective magnetic sensors 11 and 12 output sinusoidal signals with a 90° phase difference with respect to each other and the rotation angle of the rotor 1 is detected based on the two sinusoidal signals. Both magnetic sensors 11 and 12 are mounted on a board 2 indicated by dashed lines in FIG. 13.
The direction indicated by the arrow in FIG. 13 shall be deemed to be a positive rotation direction of the rotor 1. It shall also be deemed that the rotation angle of the rotor 1 increases when the rotor 1 is rotated in the positive direction, and the rotation angle of the rotor 1 decreases when the rotor 1 is rotated in the opposite direction. If θ is the rotation angle of the rotor 1, an output signal V1 of one magnetic sensor 11 is expressed as V1=A1·sin θ, and an output signal V2 of the other magnetic sensor 12 is expressed as V2=A2·sin(θ+π/2)=A2·cos θ. A1 and A2 respectively express amplitudes.
If the amplitudes A1 and A2 are deemed to be mutually equal to a value A or both signals V1 and V2 are normalized so that both amplitudes are of a certain predefined value A, one output signal V1 is expressed as V1=A·sin θ and the other output signal V2 is expressed as V2=A·cos θ. Further, if A=1, the one output signal V1 is expressed as V1=sin θ and the other output signal V2 is expressed as V2=cos θ. Here, to simplify the description, the output signals V1 and V2 of the respective magnetic sensors 11 and 12 shall be expressed as V1=sin θ and V2=cos θ.
The rotation angle θ of the rotor can be determined using both output signals V1 and V2 based, for example, on the following formula (1).
                                                        θ              =                                                tan                                      -                    1                                                  ⁡                                  (                                      sin                    ⁢                                                                                  ⁢                                          θ                      /                      cos                                        ⁢                                                                                  ⁢                    θ                                    )                                                                                                        =                                                tan                                      -                    1                                                  ⁡                                  (                                      V                    ⁢                                                                                  ⁢                                          1                      /                      V                                        ⁢                                                                                  ⁢                    2                                    )                                                                                        (        1        )            